To simplify the given expression [tex]\((6 + 4i) + (3 - 3i)\)[/tex], we need to add the real parts together and the imaginary parts together.
1. Identify the real parts:
- The real part of [tex]\(6 + 4i\)[/tex] is 6.
- The real part of [tex]\(3 - 3i\)[/tex] is 3.
2. Add the real parts:
[tex]\[
6 + 3 = 9
\][/tex]
3. Identify the imaginary parts:
- The imaginary part of [tex]\(6 + 4i\)[/tex] is [tex]\(4i\)[/tex].
- The imaginary part of [tex]\(3 - 3i\)[/tex] is [tex]\(-3i\)[/tex].
4. Add the imaginary parts:
[tex]\[
4i + (-3i) = 4i - 3i = 1i = i
\][/tex]
5. Combine the results:
[tex]\[
\text{Real part: } 9
\][/tex]
[tex]\[
\text{Imaginary part: } i
\][/tex]
Therefore, combining the real and imaginary parts, we get [tex]\(9 + i\)[/tex].
So, the simplified expression is [tex]\(9 + i\)[/tex], which corresponds to option C: [tex]\(\boxed{9 + i}\)[/tex].
